GMAT Math

The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Total number of games = 20
Number of games already played = 5
Number of games left = 15

Number of points after 5 games = 9
Number of points after 20 games = 40

So, they got to score 31 points in 15 games with the least number of wins

Here are a list of possibilities:

15 games, 10 wins and a draw = 10*3 + 1 = 31 Points
15 games, 9 wins and 4 draws = 9*3 + 4 = 31 points
15 games , 8 wins and 7 draws = 8*3 + 7 = 31 points
15 games, 7 wins and 10 draws = 7*3 + 10 = 31 points, but the total number of games is > 15 (17)

So the least number of wins to reach the 40 point mark = 8

Answer C

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It is important to realize that the number of points from the draw also count.

So, easiest way is we know draw=1, win=3 and we have 15 games left

Set up equation

win(n games) + draw(15-n games) = 31 points

3(n) + 1(15-n)= 31
3n + 15- n = 31

2n = 16, n = 8

Answer: C, 8 wins